Non-wellfounded proof theory for (Kleene+action)(algebras+lattices)

Abstract : We prove cut-elimination for a sequent-style proof system which is sound and complete for the equational theory of Kleene algebra, and where proofs are potentially non-wellfounded infinite trees. We extend these results to systems with meets and residuals, capturing 'star-continuous' action lattices in a similar way. We recover the equational theory of all action lattices by restricting to regular proofs (with cut)—those proofs that are unfoldings of finite graphs.
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Anupam Das, Damien Pous. Non-wellfounded proof theory for (Kleene+action)(algebras+lattices). Computer Science Logic (CSL), Sep 2018, Birmingham, United Kingdom. ⟨10.4230/LIPIcs.CSL.2018.19⟩. ⟨hal-01703942v3⟩

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